This section is intended to introduce various aspects of the art, which may be associated with embodiments of the disclosed techniques. This discussion is believed to assist in providing a framework to facilitate a better understanding of particular aspects of the disclosed techniques. Accordingly, it should be understood that this section is to be read in this light, and not necessarily as admissions of prior art.
Three-dimensional (3D) model construction and visualization commonly employs data stored in a data volume organized as a structured grid or an unstructured grid. Data stored in a data volume may comprise a data model that corresponds to one or more physical properties about a corresponding region that may be of interest. Physical property model construction and data visualization have been widely accepted by numerous disciplines as a mechanism for analyzing, communicating, and comprehending complex 3D relationships. Examples of physical regions that can be subjected to 3D analysis include the earth's subsurface, facility designs and the human body.
In the field of hydrocarbon exploration, analysis of a reservoir's connectivity facilitates characterizing the reservoir. Moreover, connectivity analysis may affect decisions made in all phases of hydrocarbon resource development (such as exploration and production) of an asset's life cycle. Connectivity assessments can affect decisions ranging from determining optimal well locations, to managing reservoir decisions.
In one known technique, a set of rules and processes allow geologists to identify compartments from reservoir geometry. Typically, compartment identification starts with structure maps. Structural features, stratigraphic features, and the limits of top-seal or base-seal define compartment boundaries. Without knowledge of fluid contacts, depths, pressures conditions, one can identify potential compartment boundaries from the maps based on a few simple rules of the structural and stratigraphic features. That is, one can evaluate relevance of compartment boundaries defined by top-seal or base-seal. Traditional spill points on convex-upward closures and down-dip tips of faults or other structural or stratigraphic barriers are only relevant on top-of-reservoir maps. Break-over points, including those associated with concave-upward closures and up-dip tips of faults or other structural or stratigraphic barrier, are only relevant on base-of-reservoir maps. Even though the rules to identify compartments on the structure maps are relatively simple, the process of identification typically relies on the geologists' manual identification of compartment boundaries and contact relations among boundaries based on the contour and/or cross sessions display in structural surface.
FIG. 1 is a diagram that is useful in explaining the identification of compartments using structure maps. The diagram is generally referred to by the reference number 100. The diagram 100 includes a left panel 102, a center panel 104, and a right panel 106.
The left panel 102 shows a top-seal map of the top of a reservoir. The structural contour of the top seal is represented with isolines 108, each of which represents a solid polygon of uniform depth along the top of the reservoir.
The center panel 104 shows a base-seal map of the base of the reservoir. As in the left panel, the structural contour of the bottom seal is represented with isolines 108, each of which represents a solid polygon of uniform depth along the top of the reservoir.
The right panel 106 shows a cross section taken along lines A-A′ 112 of the left panel 102 and the center panel 104. The depth contour of the top seal is shown as line 114, and the depth contour of the bottom seal is shown as line 116. The locations of the first compartment 118 and the second compartment 120 are clearly shown in the right panel 106. The dashed line in the right panel 106 shows the depth that is identified as the top of the first compartment 118. Thus, the potential compartments 118 and 120 can be manually identified by inspection of the reservoir contours of a base seal and a top seal.
Known processes of compartment identification rely on geologists' knowledge and step-by-step procedures to identify compartment boundaries first. The contacts from compartment boundaries may then be used to identify the spill points and break-over points among compartments. Furthermore, the traditional methods would make the handling of the uncertainty of the structural and stratigraphic features difficult if not impossible.
The following paragraphs provide specific examples of known techniques for processing geometric data. U.S. Pat. No. 5,966,141 to Ito, et al., discloses an animation solid that is created by an animation solid generator such that the shape of its cross section at t=t0 coincides with the shape of the contour of an object contained in a frame to be displayed at t=t0, wherein time t is set in the height z direction of the solid. For creation of this solid, topological considerations, including connected components and the tree structure of contours, are used. By chopping this solid, it is submitted that intermediate dividing can be performed. According to the disclosure, the basis of the topological geometry rests on Morse theory.
U.S. Pat. No. 6,323,863 to Shinagawa, et al., discloses that shape expressions in CAD or CG have often been carried out in polygon data. In polygon representations, the amount of data becomes very large if precision is pursued. Another shape representation utilizing the existing polygon data asset is disclosed. Polygon data showing the shape of an object is first obtained. Topological information of the object is extracted from the polygon data. Based on the information, the polygon data is converted into topological data. The inversion is carried out upon necessity.
U.S. Patent Application Publication No. 2005/0002571 by Hiraga, et al., discloses a shape analyzer that inputs a 3D representation of an object such as merchandise. A structural graph of the object is constructed by defining a continuous function on the surface of the object. The surface is then partitioned into plural areas according to the function values at the points on the surface. The areas are associated with nodes of the graph. By choosing a function that returns values invariant to rotation of the objects, the constructed graph also becomes invariant to rotation. This property is said to be important when searching for objects by shape from a shape database, as the postures of the objects are unknown when searching is performed. The analyzer is stated to be applicable to search engines for online shopping, where a user seeks goods by designating the general shape of the target.
S. Smale, “Morse Inequalities for a Dynamical System”, Bulletin of American Mathematical Society, Volume 66, No. 1 (1960), describes a topological structure of a scalar field in the continuum. According to the article, a real value function ƒ: M(a two-manifold)−>R (a Real field) is called a Morse function if it is at least twice differentiable, its values at critical points (for example, minimums, maximums, saddles) defined by ▾ƒ=0 are distinct and its Hessian matrix of second derivatives of ƒ has nonzero determinant at critical points. Moreover, the article provides a topological analysis of mathematical theory that may be useful.
The following paragraphs provide specific examples of known reservoir data analysis techniques. U.S. Patent Application Publication No. 2006/0235666 by Assa, et al, discloses methods and systems for processing data used for hydrocarbon extraction from the earth. Symmetry transformation groups are identified from sampled earth structure data. A set of critical points is identified from the sampled data. Using the symmetry groups and the critical points, a plurality of subdivisions of shapes is generated, which together represent the original earth structures. The symmetry groups correspond to a plurality of shape families, each of which includes a set of predicted critical points. The subdivisions are preferably generated such that a shape family is selected according to a best fit between the critical points from the sampled data and the predicted critical points of the selected shape family.
International Patent Application Publication No. WO2009/094064 by Meurer, et al., discloses methods, computer-readable mediums, and systems that analyze hydrocarbon production data from a subsurface region to determine geologic time scale reservoir connectivity and production time scale reservoir connectivity for the subsurface region. Compartments, fluid properties, and fluid distribution are interpreted to determine geologic time scale reservoir connectivity and production time scale reservoir connectivity for the subsurface region. A reservoir connectivity model based on the geologic time scale and production time scale reservoir connectivity for the subsurface region is constructed, wherein the reservoir connectivity model includes a plurality of production scenarios each including reservoir compartments, connections, and connection properties for each scenario. Each of the production scenarios is tested and refined based on production data for the subsurface region.
P. J. Vrolijk, et al., “Reservoir Connectivity Analysis—Defining Reservoir Connections and Plumbing”, SPE Middle East Oil and Gas Show and Conference, Kingdom of Bahrain (2005), provides that gas, oil, and water fluids in channelized or faulted reservoirs can create complex reservoir plumbing relationships. Variable hydrocarbon contacts can develop when some, but not all, fluids are in pressure communication. Reservoir Connectivity Analysis (RCA) is a series of analyses and approaches to integrate structural, stratigraphic, and fluid pressure and composition data into permissible but non-unique scenarios of fluid contacts and pressures. RCA provides the basis for fluid contact and pressure scenarios at all business stages, allowing the creation of fluid contact and segmentation scenarios earlier in an exploration or development setting, and the identification of by-passed pays or new exploration opportunities in a production setting. Combining conventional structural and fault juxtaposition spill concepts with a renewed appreciation of fluid break-over (contacts controlled by spill of pressure-driven, denser fluid, like water over a dam) and capillary leak (to define the ratio of gas and oil where capillary gas leak determines the gas-oil contact (GOC)), permissible but non-unique scenarios of the full fluid fill/displacement/spill pathways of a hydrocarbon accumulation are defined comprising single or multiple reservoir intervals.
Y. Gingold, et al., “Controlled-Topology Filtering”, Computer-Aided Design, Volume 39, Issue 8 (2007) presents an algorithm based on Critical Point analysis that postulates that the filtering result would preserve the topological features on the surface. According to the paper, many applications require the extraction of isolines and isosurfaces from scalar functions defined on regular grids. These scalar functions may have many different origins, from MRI and CT scan data to terrain data or results of a simulation. As a result of noise and other artifacts, curves and surfaces obtained by standard extraction algorithms often suffer from topological irregularities and geometric noise. While it is possible to remove topological and geometric noise as a post-processing step, in the case when a large number of isolines are of interest there is a considerable advantage in filtering the scalar function directly. While most smoothing filters result in gradual simplification of the topological structure of contours, new topological features typically emerge and disappear during the smoothing process. The paper describes an algorithm for filtering functions defined on regular 2D grids with controlled topology changes, which is stated to ensure that the topological structure of the set of contour lines of the function is progressively simplified.
P. Bremer, et al., “Maximizing Adaptivity in Hierarchical Topological Models Using Extrema Trees”, IEEE PROC-216200 (2005), discloses an adaptive hierarchical representation of the topology of functions defined over two-manifold domains. Guided by the theory of Morse-Smale complexes, dependencies between cancellations of critical points are encoded using two independent structures: a traditional mesh hierarchy to store connectivity information and a new structure called an extrema tree to encode the configuration of critical points. Extrema trees are described as providing a powerful method to increase adaptivity while using a relatively simple data structure. The resulting hierarchy is described as being relatively flexible. In particular, the resulting hierarchy is stated to be guaranteed to be of logarithmic height.
A. Gyulassy, et al., “A Topological Approach to Simplification of Three-dimensional Scalar Functions”, IEEE Transactions Visualization and Computer Graphics (2006), describes a combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.
G. H. Weber, et al., “Topology-controlled Volume Rendering”, IEEE Transactions Visualization and Computer Graphics (2007), discloses that topology provides a foundation for the development of mathematically sound tools for processing and exploration of scalar fields. Existing topology-based methods can be used to identify interesting features in volumetric data sets, to find seed sets for accelerated isosurface extraction, or to treat individual connected components as distinct entities for isosurfacing or interval volume rendering. A framework for direct volume rendering based on segmenting a volume into regions of equivalent contour topology is described, applying separate transfer functions to each region. Each region corresponds to a branch of a hierarchical contour tree decomposition, and a separate transfer function can be defined for it. A volume rendering framework and interface where a unique transfer function can be assigned to each subvolume corresponding to a branch of the contour tree. Also disclosed is a runtime method for adjusting data values to reflect contour tree simplifications. Purported to be disclosed is an efficient way of mapping a spatial location into the contour tree to determine the applicable transfer function. Also stated to be disclosed is an algorithm for hardware accelerated direct volume rendering that visualizes the contour tree-based segmentation at interactive frame rates using graphics processing units (GPUs) that support loops and conditional branches in fragment programs.
H. Carr, “Contour Tree Simplification With Local Geometric Measures”, MIT, 14th Annual Fall Workshop on Computational Geometry (2004), discloses that the contour tree, an abstraction of a scalar field that encodes the nesting relationships of isosurfaces, has several potential applications in scientific and medical visualization, but noise in experimentally-acquired data results in unmanageably large trees. Geometric properties of the contours are attached to the branches of the tree and simplification by persistence is applied to reduce the size of contour trees while preserving features of the scalar field.